# Logic problem--HELP

There are three baskets sitting next to each other on a
high shelf so that you cannot see the contents of any
basket. Under the first basket is a sign that says APPLES.
Under the second basket is a sign that says ORANGES,
and under the third basket is a sign that says APPLES
AND ORANGES. Each basket is incorrectly labeled.
One basket contains all apples, one all oranges, and one a
combination of apples and oranges. Is it possible to reach
up on the shelf and without looking into any of the
baskets select one piece of fruit and on the basis of
knowing what that piece of fruit is correctly label all
three baskets? Explain your reasoning

### Re: Logic problem--HELP

can i have a hint? i am not a math major

### Re: Logic problem--HELP

It is an important fact that you know that *all three* jars are labeled incorrectly. Just go through each possibility and see what you can deduce. For example, suppose you pick a fruit from the jar labeled "Apples" and it's an apple. Can you conclude anything? How about if it's an orange? Do this for all three jars and I think you'll figure it out.

### Re: Logic problem--HELP

Yes.

Too easy for a hint. Just work it out.

### Re: Logic problem--HELP

froggn4life,
I'll give it a try, more for the method than anything else.
I was taught to first write down the information in the problem.
There are 3 baskets 1) Not A, 2) Not O, and 3) Not A&O, but these baskets contain All A, All O, or A&O.
Now we "deduce" the possibilities:
The basket mislabeled All A, could contain All O or A&O.
The basket mislabeled All O, could contain All A or A&O.
The basket mislabeled A&O, could contain All A or All O.
Thirdly, we consider what the test results could be:
If we pick a piece of fruit out of the basket mislabeled All A,
And it's an A, then basket Not All A contains A&O, Not All O contains All A, and Not A&O contains All O.
And it's an O, then basket Not A could still contain All O or A&O.
If we pick a piece of fruit out of the basket mislabeled All O,
And it's an A, then basket Not All O, could contain All A or A&O.
And it's an O, then basket Not All O, contains A&O. Not All O contains All A, and Not All A contains All O.
If we pick a piece of fruit out of the basket mislabeled A&O,
And it's an A, then basket Not A&O contains All A, Not All O contains A&O, and Not All A contains All O.
And it's an O, then basket Not A&O contains All O. And Not All A contains A&O, And Not All A contains All O.
Therefore picking a piece of fruit out of basket Not A&B, will tell us what's in all three baskets.
I'd like to sleep on this and reverify it; but I don't think it'll still be there after I log off.
This sounds like Boolean algebra to me. Could a truth table be drawn up to verify the reasoning?
- marie

### Re: Logic problem--HELP

froggn4life,
Please give me a little feedback.
Did you understand my answer? I'm thinking, it might have been too condensed.
Was it correct as far as you know? I didn't know the answer in advance!
With my best wishes,
- marie